Low-frequency radio navigation system

ABSTRACT

Systems and methods for a low-frequency radio navigation system are described. The system may include a transmitter comprising a base coded modulator configured to generate a base modulation and a data coded modulator configured to generate a data modulation; wherein the transmitter radiates a continuous, constant-power chirped-FM spread spectrum signal, comprising: the base modulation; and the data modulation, wherein the data modulation is orthogonal to the base modulation. The system may also include a receiver comprising a digital signal processor, wherein at least one matched filter coupled to the digital signal processor, the at least one matched filter configured to decode said base modulation and data-encoded modulation and provide a correlation function for received signals received from at least three geographically-spaced transmitters.

This application is a continuation of U.S. application Ser. No.16/428,620, filed May 31, 2019, for LOW-FREQUENCY RADIO NAVIGATIONSYSTEM, which is incorporated in its entirety herein by reference.

BACKGROUND OF THE INVENTION 1. Field of the Invention

The present invention relates generally to low-frequency radionavigation, and more specifically to low-frequency radio navigationutilizing continuous signal transmission.

2. Discussion of the Related Art

Various systems and processes are known in the art for low-frequencyradio navigation utilizing continuous signal transmission.

Vulnerabilities in Global Navigation Satellite Systems (GNSS), forexample the US Global Positioning System, highlight the need for analternative, robust and terrestrial-based Position, Navigation and Time(PNT) delivery system.

One existing proposal is called e-Loran, based on the former Loran-Cwhich was designed in the 1950s and operational in the USA until 2011,when the US Government turned off the system. e-Loran claims about thesame level of PNT performance that Loran-C provided in 1962. In apresentation on the system, the only real claimed difference betweenLoran-C and e-Loran is a low rate (30 bps) data channel. e-Loran isstill the same basic 60-year-old technology from 1958 used in Loran-C.

There is a need for a real upgrade in capability and cost/performancebased on modern technologies and using the same 90-110 kHz band formerlyused by Loran-C. Loran-C and e-Loran are pulsed systems with peakenvelope powers in the hundreds of kW up to MW range. While this soundsimpressive, they use low duty cycles, and to deal with skywaveinterference, they require using the (lower power) leading edge of thesignal to detect a particular ‘reference crossing’ which being at −6 dBrelative to the peak, means that for all purposes the actual useful peakpower is more like tens to a few hundred kW, and the average power lessthan 1% of that—perhaps a kilowatt.

SUMMARY

A low-frequency radio navigation system is described. The system mayinclude a transmitter comprising a base coded modulator configured togenerate a base modulation, a data coded modulator configured togenerate a data modulation, and the transmitter radiates a continuous,constant-power chirped-FM spread spectrum signal, comprising: the basemodulation and the data modulation, wherein the data modulation isorthogonal to the base modulation.

In some examples of the low-frequency radio navigation system describedabove, said base modulation comprises a periodic frequency modulation(FM) waveform.

In some examples of the low-frequency radio navigation system describedabove, said base modulation is the periodic frequency modulation (FM)waveform selected from the group of waveforms consisting of a trianglewaveform, a ramp (sawtooth) waveform, a sinusoid waveform, andcombinations of one or more of such waveforms.

In some examples of the low-frequency radio navigation system describedabove, said data modulation comprises a continuous frequency-shiftkeying signal.

In some examples of the low-frequency radio navigation system describedabove, said continuous frequency-shift keying signal encodes at leastone data symbol per period of said periodic frequency modulation (FM)waveform.

In some examples of the low-frequency radio navigation system describedabove, said continuous frequency-shift keying signal is shaped with awindow function.

In some examples of the low-frequency radio navigation system describedabove, said window function is selected from the group of functionsconsisting of Hann, Hamming, Blackman and Nutall.

Some examples of the transmitter, receiver, method, and low-frequencyradio navigation system described above may further include a receivercomprising a matched filter configured to process the continuous,constant-power chirped-FM spread spectrum signal.

In some examples of the low-frequency radio navigation system describedabove, said matched filter yields correlation of the base modulation andthe data modulation to defined reference modulations. In some examplesof the low-frequency radio navigation system described above, saidreceiver further comprises: means for determining a relative time ofarrival of said continuous, constant-power chirped-FM spread spectrumsignal from the transmitter within one microsecond; means fordetermining which data symbol values are likely encoded in saidcontinuous, constant-power chirped-FM spread spectrum signal; and meansfor determining whether data symbols encoded in said continuous,constant-power chirped-FM spread spectrum signal are corrupted.

In some examples of the low-frequency radio navigation system describedabove, said transmitter shares a frequency band and carrier frequencywith a plurality of other transmitters in an array of transmitters. Insome examples of the low-frequency radio navigation system describedabove, a base modulation frequency for each transmitter in the array oftransmitters is selected from a plurality of values. In some examples ofthe low-frequency radio navigation system described above, the receivercomprises at least one additional matched filer for each base modulationfrequency. In some examples of the low-frequency radio navigation systemdescribed above, signals from said transmitter and said plurality ofother transmitters are identified and separated in said receiver.

In some examples of the low-frequency radio navigation system describedabove, forward error correction is used by said receiver to compensatefor symbol errors resulting from received noise, jamming or interferingsignals, or signals from other transmitters in the system. In someexamples of the low-frequency radio navigation system described above, aplurality of parity symbols are appended to each block of data symbols.In some examples of the low-frequency radio navigation system describedabove, likely corrupted symbols (data or parity) are marked as erased.In some examples of the low-frequency radio navigation system describedabove, wherein erased symbols are corrected, requiring a single paritysymbol each to correct. In some examples of the low-frequency radionavigation system described above, wherein errorring symbols, notdetected a priori as corrupted, are detected and corrected, requiringtwo parity symbols each to detect and correct. In some examples of thelow-frequency radio navigation system described above, wherein forwarderror correction code may be a Reed-Solomon code.

In some examples of the low-frequency radio navigation system describedabove, said data modulation includes operational data comprising timingoffsets, nominal transmitter antenna center position, and otherinformation required for determination of position, navigation and time.

In some examples of the low-frequency radio navigation system describedabove, said data modulation includes authentication data for allowing areceiver to validate that a message was sent by an authorizedtransmitter and was not corrupted or modified.

In some examples of the low-frequency radio navigation system describedabove, said data modulation includes differential corrections thatencode time-varying signal propagation differences and other systemerrors from nominal, allowing a receiver to correct these errorsresulting in greater accuracy.

In some examples of the low-frequency radio navigation system describedabove, said data modulation includes altimeter corrections used by areceiver along with a local barometric pressure measurement to provide3-dimensional position information.

In some examples of the low-frequency radio navigation system describedabove, transmit energy is spread over a fraction of a frequency bandwhile minimizing power outside of the frequency band, wherein saidfraction of the frequency band is 50% or greater and said power outsideof said frequency band is less than 1%.

In some examples of the low-frequency radio navigation system describedabove, said fraction is greater than 80%, and said power outside of thefrequency band less than 0.1%.

In some examples of the low-frequency radio navigation system describedabove, active transmit power is constant.

In some examples of the low-frequency radio navigation system describedabove, the transmitter is turned off periodically to synchronize areceiver to the transmitter.

In some examples of the low-frequency radio navigation system describedabove, the transmitter is turned off periodically wherein a transmittingsite of the transmitter receives signals from other transmitters duringa period when the transmitter is turned off, whereby the transmittingsite receives the signals without interference from the transmitter.

In some examples of the low-frequency radio navigation system describedabove, the transmitter is turned off periodically wherein a receiverreceives signals from other transmitters during a period when thetransmitter is turned off, whereby the receiver receives the signalswithout interference from the transmitter.

In some examples of the low-frequency radio navigation system describedabove, the transmitter comprises a power output stage using directdigital synthesis.

In some examples of the low-frequency radio navigation system describedabove, said direct digital synthesis comprises a stepped voltagewaveform.

In some examples of the low-frequency radio navigation system describedabove, said stepped voltage waveform comprises 4 to 64 steps per carriercycle.

In some examples of the low-frequency radio navigation system describedabove, said stepped voltage waveform comprises 10 to 20 steps percarrier cycle.

Some examples of the transmitter, receiver, method, and low-frequencyradio navigation system described above may further include a processorcontrolling timing of steps of said stepped voltage waveform.

In some examples of the low-frequency radio navigation system describedabove, said processor is selected from the group consisting of a fieldprogrammable gate array, a digital signal processor, a microprocessor,and a finite state machine.

In some examples of the low-frequency radio navigation system describedabove, said transmitter comprises a band-pass filter stage between saidpower output stage and an antenna.

In some examples of the low-frequency radio navigation system describedabove, said band-pass filter stage is optimized to cancel out part of areactive component of antenna impedance across at least parts of afrequency band, wherein a ratio of reactive-to-active power is less than3 at band edges of the frequency band after said band-pass filter stage.

In some examples of the low-frequency radio navigation system describedabove, a power supply voltage of said power output stage is continuallyadjusted to compensate for varying antenna impedance with frequency.

In some examples of the low-frequency radio navigation system describedabove, signal parameters are continually adjusted to compensate forphase variations of said power output stage, said band-pass filterstage, and an antenna system.

In some examples of the low-frequency radio navigation system describedabove, an amount of an adjustment of the signal parameters is determinedby measuring an antenna current phase and magnitude and determining saidamount of the adjustment.

In some examples of the low-frequency radio navigation system describedabove, a determination of adjustments is performed by one or anycombination of a field programmable gate array, a digital signalprocessor, a microprocessor, or other computing device.

A low-frequency radio navigation system is described. The system mayinclude a receiver comprising a digital signal processor and at leastone matched filter coupled to the digital signal processor, the at leastone matched filter configured to decode said base modulation anddata-encoded modulation and provide a correlation function for receivedsignals received from at least three geographically-spaced transmitters.

In some examples of the low-frequency radio navigation system describedabove, the digital signal processor receives and decodes receivedsignals, which, after decoding, are re-created by digital synthesis andsubtracted from other received signals, and processed to determine othertransmitted signals, wherein co-channel interference is reduced.

In some examples of the low-frequency radio navigation system describedabove, said digital signal processor is configured to use forward errorcorrection to compensate for symbol errors.

In some examples of the low-frequency radio navigation system describedabove, said receiver comprises a multi-element antenna configured toallow a received signal to be processed and combined to steer a null ormaximum in a direction of an undesired or desired transmitter, andfurther configured to allow the received signal to be processed in sucha way as to determine an approximate direction of a given transmitter.

In some examples of the low-frequency radio navigation system describedabove, the digital signal processor receives and decodes receivedsignals, to provide position, navigation, or timing information.

In some examples of the low-frequency radio navigation system describedabove, said digital signal processor receives and decodes receivedsignals, to provide information selected from the group consisting of:position, course, course error, heading, velocity, acceleration, speed,time, distance to a next waypoint, a projected change in course orheading, time and frequency, message authentication.

A method for determining the voltage step timing in a direct digitalstepped synthesizer in a transmitter is described. The method mayinclude receiving values for modulating signal parameters, receivingvalues for modulation signal corrections, receiving a precise timereference signal, determining resulting modulation parameters, includingfrequency and phase angle, determining times when the direct digitalstepped synthesizer should step to next levels, and outputting one or aplurality of digital signals for controlling an output of said directdigital stepped synthesizer, as a function of time.

An apparatus for determining the voltage step timing in a direct digitalstepped synthesizer in a transmitter is described. The apparatus mayinclude a processor, memory in electronic communication with theprocessor, and instructions stored in the memory. The instructions maybe operable to cause the processor to receive values for modulatingsignal parameters, receive values for modulation signal corrections,receive a precise time reference signal, determine resulting modulationparameters, including frequency and phase angle, determine times whenthe direct digital stepped synthesizer should step to next levels, andoutput one or a plurality of digital signals for controlling an outputof said direct digital stepped synthesizer, and as a function of times.

A non-transitory computer readable medium storing code for determiningthe voltage step timing in a direct digital stepped synthesizer in atransmitter is described. In some examples, the code comprisesinstructions executable by a processor to: receive values for modulatingsignal parameters, receive values for modulation signal corrections,receive a precise time reference signal, determine resulting modulationparameters, including frequency and phase angle, determine times whenthe direct digital stepped synthesizer should step to next levels, andoutput one or a plurality of digital signals for controlling an outputof said direct digital stepped synthesizer, and as a function of times.

In some examples of the method, apparatus, and non-transitory computerreadable medium described above, values for said signal parameters aredetermined as continuous time functions.

In some examples of the method, apparatus, and non-transitory computerreadable medium described above, values for said signal parameters aredetermined as sampled points.

A method for estimating signal corrections is described. The method mayinclude receiving values for signal parameters, receiving values forsignal corrections from a previous calculation, if available, samplingantenna current from a transducer, as an analog signal, digitizing saidanalog signal with an analog-to-digital converter, synchronized to aprecise time reference signal, determining values of signal parametersof an antenna current, comparing signal parameters of said antennacurrent to said signal parameters, determining values of said signalcorrections, outputting values of said signal corrections, and storingvalues of said signal corrections in a memory device.

An apparatus for estimating signal corrections is described. Theapparatus may include a processor, memory in electronic communicationwith the processor, and instructions stored in the memory. Theinstructions may be operable to cause the processor to receive valuesfor signal parameters, receive values for signal corrections from aprevious calculation, if available, sample antenna current from atransducer, as an analog signal, digitize said analog signal with ananalog-to-digital converter, synchronized to a precise time referencesignal, determine values of signal parameters of an antenna current,compare signal parameters of said antenna current to said signalparameters, determine values of said signal corrections, output valuesof said signal corrections, and store values of said signal correctionsin a memory device.

A non-transitory computer readable medium storing code for estimatingsignal corrections is described. In some examples, the code comprisesinstructions executable by a processor to: receive values for signalparameters, receive values for signal corrections from a previouscalculation, if available, sample antenna current from a transducer, asan analog signal, digitize said analog signal with an analog-to-digitalconverter, synchronized to a precise time reference signal, determinevalues of signal parameters of an antenna current, compare signalparameters of said antenna current to said signal parameters, determinevalues of said signal corrections, output values of said signalcorrections, and store values of said signal corrections in a memorydevice.

A low-frequency radio navigation system is described. The system mayinclude a first transmitter at a first location, the first transmittercomprising: a first base coded modulator configured to generate a firstbase modulation; and a first data coded modulator configured to generatea first data modulation; wherein the first transmitter radiates a firstcontinuous, constant-power chirped-FM spread spectrum signal,comprising: the first base modulation; and the first data modulation,wherein the first data modulation is orthogonal to the first basemodulation, a second transmitter at a second location, the secondtransmitter comprising: a second base coded modulator configured togenerate a second base modulation; and a second data coded modulatorconfigured to generate a second data modulation; wherein the secondtransmitter radiates a second continuous, constant-power chirped-FMspread spectrum signal, comprising: the second base modulation; and thesecond data modulation, wherein the second data modulation is orthogonalto the second base modulation, and a third transmitter at a thirdlocation, the third transmitter comprising: a third base coded modulatorconfigured to generate a third base modulation; and a third data codedmodulator configured to generate a third data modulation; wherein thethird transmitter radiates a third continuous, constant-power chirped-FMspread spectrum signal, comprising: the third base modulation; and thethird data modulation, wherein the third data modulation is orthogonalto the third base modulation.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an example of a low-frequency radio navigation system inaccordance with aspects of the present disclosure.

FIG. 2 shows an example of a transmitter in accordance with aspects ofthe present disclosure.

FIG. 3 shows an example of a receiver in accordance with aspects of thepresent disclosure.

FIG. 4 shows an example of modulation signals of a transmitter inaccordance with aspects of the present disclosure.

FIG. 5 shows an example of carrier signals of a transmitter inaccordance with aspects of the present disclosure.

FIG. 6 shows an example of active/reactive power ratios for an antennaand a transmitter in accordance with aspects of the present disclosure.

FIGS. 7 and 8 show examples of a process for low-frequency radionavigation utilizing continuous signal transmission in accordance withaspects of the present disclosure.

DETAILED DESCRIPTION

The following description is not to be taken in a limiting sense, but ismade merely for the purpose of describing the general principles ofexemplary embodiments. The scope of the invention should be determinedwith reference to the claims.

Reference throughout this specification to “one embodiment,” “anembodiment,” or similar language means that a particular feature,structure, or characteristic described in connection with the embodimentis included in at least one embodiment of the present invention. Thus,appearances of the phrases “in one embodiment,” “in an embodiment,” andsimilar language throughout this specification may, but do notnecessarily, all refer to the same embodiment.

Furthermore, the described features, structures, or characteristics ofthe invention may be combined in any suitable manner in one or moreembodiments. In the following description, numerous specific details areprovided, such as examples of programming, software modules, userselections, network transactions, database queries, database structures,hardware modules, hardware circuits, hardware chips, etc., to provide athorough understanding of embodiments of the invention. One skilled inthe relevant art will recognize, however, that the invention can bepracticed without one or more of the specific details, or with othermethods, components, materials, and so forth. In other instances,well-known structures, materials, or operations are not shown ordescribed in detail to avoid obscuring aspects of the invention.

The present disclosure describes a resilient terrestrial PNT systemusing a novel modulation scheme, allowing the use of continuous signaltransmission (CW or ‘continuous wave’), thereby allowing a much lowerpeak transmitter power in the range of 1-10 kW. Lower peak powertranslates into lower peak voltages, lower cost and greater reliability.CW navigation systems have been proposed in the past, but thoseimplementations suffered from skywave problems with no way to fix them.Loran-C offers a way to overcome skywave interference, but atsignificant cost.

The proposed system uses ‘chirp FM’ technology originally developed forradars by the US military. With this technology, a received FM signal isprocessed using a ‘matched filter,’ which compresses the continuousreceived energy into a series of narrow pulses. These narrow pulsesprovide excellent resolution in the time domain, required for accuratedetermination of position and time.

This system makes use of 100% of the transmitted power, 100% of the timeinstead of 25% of the power, 1% of the time. This provides superiorsignal to noise ratio and similar rejection of skywave interference, atlower system cost. Compressing the signal in the receiver using digitalsignal processing is far more practical than generating an equivalentpulse directly in the transmitter.

Due to the ‘pulse compression ratio’ of such a system, a 10 kW CWtransmitter develops an effective pulsed transmit power of 1-2megawatts, without dealing with the resulting difficulties of highpulsed power at the transmit site: the CW-FM transmitter signal is‘compressed’ into a series of short pulses in the receiver by signalprocessing. The transmitter itself sees only the modest power CW-FMsignal.

Using slightly different waveshapes in a single transmitter to encodemessage data (300-1 k bps), the subject invention further provides amedium-bandwidth data channel with sufficient capacity to providepremium services such as authentication and differential corrections.

Spoofing resistance results from the fact that low frequency (˜100 kHz)signals are inherently difficult to get into the air, and high transmitpower is required to overcome the extremely high level of atmosphericnoise in the LF band, as much as 140 dB (power ratio:100,000,000,000,000 times) above thermal noise; see e.g. ITU-RRecommendation P.372-13-2016. Efficient antennas at 100 kHz are quitelarge, requiring 15-60 Ha (40-160 acres) of space to put in place. Theytypically need towers on the order of 220 m or 720 feet tall, which costaround $300,000-400,000 each (depending on terrain) and cannot be builtquickly, nor without being detected by means of remote sensing, such assatellite imaging.

Smaller antennas (e.g., the size of a GNSS receive patch, 25 mm square)work well to receive low-frequency signals, but to efficiently transmita signal requires an antenna that is a modest proportion of a wavelengthin dimension. The wavelength of the 100 kHz signal is 3 km; aquarter-wave vertical tower (the ‘ideal’ transmitting antenna) istherefore about 750 m or 2500 ft. tall. This is not practical. A typicalLoran-C antenna design uses a 625′ (190 m) mast. This is 1/16 of awavelength; shorter antennas do not radiate efficiently. (The sameparadigm also applies to AM broadcasting . . . tall transmit towers areused, but a receiver can have a tiny ferrite antenna or even less, andwork fine. AM wavelengths are around 1/10 of 100 kHz-200 to 600 meters.)

A spoofer or jammer would need to efficiently transmit a powerful signalin one or better, several locations if he hoped to attack such a system.This is easy to do with GNSS—the wavelength is about 19 cm so atransmitter the size of a ballpoint pen can have an efficient radiator(and many GNSS jammers look very much like a pen). This is much harderto do at a wavelength of 3 km, particularly so in any manner pretendingto be covert or rapid-response.

FIG. 1 shows an example of a low-frequency radio navigation system 100in accordance with aspects of the present disclosure. Specifically, FIG.1 shows a low-frequency radio navigation system 100 based on chirpedspread-spectrum modulation. This system includes a plurality oftransmitters 110, arranged in a geographically-optimized patternintended to provide signals to receivers 115 located in a certain areaof service, such that any such receiver 115 is able to receive at leastthree simultaneous signals from different transmitters 110, andpreferably more. It also includes one or more receivers 115, whichobtain precise position, navigation or time information by decoding thesignals received from the transmitters 110. The system may also includeone or more control center(s) 105.

The transmitters 110 radiate a continuous, constant-power chirped-FMsignal, comprising a base modulation, which provides the benefit ofspreading the signal and then allowing it to be compressed to a narrowequivalent-time pulse, achieving high resolution in the time domain andallowing signals from the plurality of transmitters 110 to be‘separated’ from each other in the receiver 115; and a data modulation,which can be used to send information from the transmitters 110 to thereceivers 115. This information includes basic navigation and timinginformation, and ancillary services such as altimeter corrections,authentication codes, and corrections for radio propagation parameters.

The base modulation and the data modulation are ‘orthogonal,’ whichmeans that they can be combined in the transmitter 110 withoutsignificant effect on each other, and then separated in the receiver 115using appropriate signal processing. The base modulation is a periodicsignal, for example, a sine wave, triangle wave, ramp or somecombination of them. The data modulation is, for example, a shapedfrequency-shift keying signal with one or more possible waveshapes percycle of the base modulation, each state corresponding to a particulartransmitted data symbol.

For example, a particularly advantageous choice is 8 states (waveshapes)for every half period of a sinusoidal base modulation. This allows one3-bit symbol to be transmitted every half period, or two symbols (total6 bits) each period of the base modulation. The ‘shaping’ can be any ofa wide range of functions, for example the well-known ‘window functions’as are commonly used in spectral analysis: Hann, Blackman, etc. Shapingallows the spectrum of the resulting signal to be controlled, meetingthe requirement of efficient spectral utilization.

The receivers 115 contain a bank of ‘matched filters,’ whose function isto compress the received signal comprising the sum of the signalstransmitted by the plurality of transmitters 110 in the system into aseries of pulses, each of which contains embedded (a) time or phaseinformation, relative to a local clock signal in the receiver 115; (b)identification of the transmitter 110 from which the signal was sent;and (c) data symbol(s) encoded in that pulse. The matched filtersprovide the function of ‘correlation,’ i.e., they embody an impulseresponse which is the inverse of the transmitted signal. For a pluralityof transmitters 110, each transmitting one of several data symbols, abank of filters is required having the number of individual filtersequal to the product of the number of transmitters 110 and the number ofpossible data states (symbols), e.g. 8 for a 3-bit symbol set. For 10transmitter tracking channels and a 3-bit symbol set, 80 filters(correlators) are needed.

The information coming from the matched filter bank also allows thedetection of potentially corrupted data symbols. Such corruption couldcome from interfering signals, or from interactions between the signalsfrom the separate transmitters 110.

The transmitters 110 (and receivers 115) in this system operate onsingle shared frequency allocation, which is why it is important to usea form of modulation which offers low auto-correlation andcross-correlation properties, thus maximizing the ability of thereceiver 115 to discriminate between the signals originating from thenearby transmitters 110. One beneficial way to do this is to use acommon modulation wave shape (a sinusoid, for instance) with differentmodulation rates. This allows the signals to be separated in thereceiver 115, due to the differences in the impulse responses of thefilters in the matched filter bank.

Because of noise, interfering signals, and imperfect separation of thesignals in the matched filter bank, errors in decoding the data symbolswill occasionally occur. Thus, such a system may beneficially use someform of forward error correction, such as Reed-Solomon coding, which canboth detect and correct errors in the decoded symbols. It isadvantageous if the receiver 115 can identify some or most of thesymbols that are possibly corrupted, because forward error-correctioncodes are more efficient when only correcting, rather than detecting andcorrecting, errors. Matched filter banks can sometimes identify suchpotentially corrupted signals, for instance, by observing that no oneoutput pulse clearly dominates (matches the possibilities) in thecomparison scheme.

This system provides nearly-optimum utilization of the frequencyallocation, because when the FM deviation and the base modulationparameters are carefully chosen, the resulting signal energy spectrum(in the frequency domain) has a fairly uniform distribution across mostof the allocation, dropping sharply at the band edges. This contrasts topulse amplitude modulation, in which the energy distribution drops offonly slowly outside of the ‘useful’ band. Shaped pulses improve thesituation somewhat, but cannot approach the spectral efficiency ofoptimized FM. For particularly advantageous embodiments of thisinvention, for instance an FM deviation of +/−8.8 kHz at a basesinusoidal modulation rate of 100-166 Hz, with two 3-bit symbols percycle having an integrated phase deviation of +/− (2, 6, 10, or 14)πradians shaped with a Blackman window, 99.99% of the signal energy maybe contained within the +/−10 kHz allocated band, while using 90% of theallocated band.

While the transmitters 110 nominally operate continuously and atconstant RF power, it may be advantageous to turn each transmitter 110off periodically, providing the following benefits: (a) to allow symbolsynchronization; (b) to allow a transmitter 110 site to ‘listen’ to itsnearby peers without being overloaded by its own signal; and (c) toallow a receiver 115 to listen to distant transmitters 110 without beingoverloaded by a strong, nearby transmitter 110. A receiver 115's abilityto listen to distant transmitters 110 in the presence of a strong nearbysignal (i.e. its dynamic range) may be further extended by using eitheror both (a) active cancellation of the nearby signal, i.e. subtracting afacsimile of that signal before further processing; and/or (b) using anantenna which has the ability to electronically ‘steer’ a ‘null’ in thedirection of the nearby transmitter 110.

Such an antenna may be constructed, for instance, as taught in U.S. Pat.No. 3,031,663, in which two similar magnetic windings are arranged on asquare slab of ferrite material at right angles to each other. Theoutput of the windings may be summed with different weighting factors,where the weighting factors correspond to the sine and cosine of adesired steering angle. This will produce a figure-8 pattern, which hasbroad maxima in two opposing directions, and narrow minima (nulls) at 90degree angles to the maxima. U.S. Pat. No. 4,087,187 further teaches theenhancement of adding a signal derived from an element sensitive toelectric fields (the ferrite windings are sensitive to magnetic fields),which converts the figure-8 pattern to a cardioid pattern, having asingle null opposite an even broader maximum.

Such antennas may also be used to implement a form of automaticdirection finding, where the signals from the two (or three) elementsare compared to each other, and the direction of arrival can bedetermined mathematically. This information can be used to find aninitial, approximate position fix which can accelerate acquisition andresolve uncertainties in certain position solutions.

An efficient and elegant means to build the transmitter 110 of such aradionavigation system is to synthesize the output signal directly inthe power stage, without the need for intervening amplification steps.With today's power electronics, generating a signal of tens of kilowattsat ˜100 kHz is a straightforward exercise for one skilled in therelevant arts. One particularly favorable implementation uses a steppedvoltage waveform, which can be generated simply with MOSFET powerswitches and simple series combiners, such as transformers with theirsecondary windings connected in series. The relative magnitudes of thesteps is fixed, corresponding to a simple series of phase angles acrossone cycle of the output signal, and the transmitter 110 stepscontinuously from one step to the next, thus synthesizing a steppedapproximation to a sine wave. The timing of each step may be preciselycontrolled, allowing both the frequency and phase angle of the generatedsignal to be determined with very fine resolution by an appropriatecontroller.

Such a waveform (stepped approximation to a sine wave) containsharmonics of the fundamental frequency. To avoid unnecessaryinterference with other spectrum users, a band-pass filter should beincorporated between the stepped power stage and the antenna, to rejectthe harmonics. Fortuitously, the band-pass filter can also be optimizedto cancel part of the antenna system's reactive impedance at frequenciesaway from resonance, thus improving the antenna system's usablebandwidth.

Even so, the antenna (being smaller than the ‘ideal’ quarter wavemonopole) inevitably has a bandwidth narrower than the frequencyallocation, which makes operating at constant transmitter 110 power(across the allocation) more difficult. But, since at any instant intime, the transmitter 110 operates at a single frequency, the dc voltagefeeding the switched power stage can be adjusted, so that the antennacurrent (which produces the radiated power by acting in concert with theantenna's radiation resistance, P=I²R) may be controlled appropriately.Likewise, the phase angle of the stepped synthesizer may be adjusted tocompensate for the remaining reactive impedance of the antennasystem/band-pass filter combination.

This creates a form of ‘active antenna tuner’ which results in constantradiated power across a bandwidth several times greater than the nominalVSWR bandwidth of the antenna system itself. By continually adjustingthe power-stage supply voltage along with the phase compensation, theantenna current can be maintained at the correct magnitude and phaseangle at all times. This is further facilitated using an antenna-currentsensing system, which is connected in such a way as to provide afeedback signal, which allows the actual antenna current to be sensedand compared to the desired antenna current, thus permitting continuous,real-time adjustment of the power-supply voltage and phase-anglecompensation factors by the controller.

Thus, low-frequency radio navigation system 100 may comprise a firsttransmitter 110 at a first location, the first transmitter 110including: a first base coded modulator configured to generate a firstbase modulation; and a first data coded modulator configured to generatea first data modulation; where the first transmitter 110 radiates afirst continuous, constant-power chirped-FM spread spectrum signal,including: the first base modulation; and the first data modulation,where the first data modulation is orthogonal to the first basemodulation.

Low-frequency radio navigation system 100 may also comprise a secondtransmitter 110 at a second location, the second transmitter 110including: a second base coded modulator configured to generate a secondbase modulation; and a second data coded modulator configured togenerate a second data modulation; where the second transmitter 110radiates a second continuous, constant-power chirped-FM spread spectrumsignal, including: the second base modulation; and the second datamodulation, where the second data modulation is orthogonal to the secondbase modulation.

Low-frequency radio navigation system 100 may also comprise a thirdtransmitter 110 at a third location, the third transmitter 110including: a third base coded modulator configured to generate a thirdbase modulation; and a third data coded modulator configured to generatea third data modulation; where the third transmitter 110 radiates athird continuous, constant-power chirped-FM spread spectrum signal,including: the third base modulation; and the third data modulation,where the third data modulation is orthogonal to the third basemodulation.

In some examples, the transmitter 110 radiates a continuous,constant-power chirped-FM spread spectrum signal, including: the basemodulation; and the data modulation, where the data modulation isorthogonal to the base modulation. In some examples, the transmitter 110shares a frequency band and carrier frequency with a set of othertransmitters 110 in an array of transmitters 110. In some examples,signals from the transmitter 110 and the set of other transmitters 110are identified and separated in the receiver 115. In some examples,transmit energy is spread over a fraction of a frequency band whileminimizing power outside of the frequency band, where the fraction ofthe frequency band is 50% or greater and the power outside of thefrequency band is less than 1%.

In some examples, the fraction is greater than 80%, and the poweroutside of the frequency band less than 0.1%. In some examples, activetransmit power is constant. In some examples, the transmitter 110 isturned off periodically to synchronize a receiver 115 to the transmitter110. In some examples, the transmitter 110 is turned off periodicallywhere a transmitting site of the transmitter 110 receives signals fromother transmitters 110 during a period when the transmitter 110 isturned off, whereby the transmitting site receives the signals withoutinterference from the transmitter 110. In some examples, the transmitter110 is turned off periodically where a receiver 115 receives signalsfrom other transmitters 110 during a period when the transmitter 110 isturned off, whereby the receiver receives the signals withoutinterference from the transmitter 110.

In some examples, the transmitter 110 includes a power output stageusing direct digital synthesis. In some examples, the direct digitalsynthesis includes a stepped voltage waveform. In some examples, thestepped voltage waveform includes 4 to 64 steps per carrier cycle. Insome examples, the stepped voltage waveform includes 10 to 20 steps percarrier cycle. In some examples, the transmitter 110 includes aband-pass filter stage between the power output stage and an antenna. Insome examples, the band-pass filter stage is optimized to cancel outpart of a reactive component of antenna impedance across at least partsof a frequency band, where a ratio of reactive-to-active power is lessthan 3 at band edges of the frequency band after the band-pass filterstage.

In some examples, a power supply voltage of the power output stage iscontinually adjusted to compensate for varying antenna impedance withfrequency. In some examples, signal parameters are continually adjustedto compensate for phase variations of the power output stage, theband-pass filter stage, and an antenna system. In some examples, anamount of an adjustment of the signal parameters is determined bymeasuring an antenna current phase and magnitude and determining theamount of the adjustment. In some examples, a determination ofadjustments is performed by one or any combination of a fieldprogrammable gate array, a digital signal processor, a microprocessor,or other computing device.

Transmitter 110 may receive values for modulating signal parameters;receive values for modulation signal corrections; receive a precise timereference signal; determine resulting modulation parameters, includingfrequency and phase angle; determine times when the direct digitalstepped synthesizer should step to next levels; and output one or a setof digital signals for controlling an output of the direct digitalstepped synthesizer, as a function of time. In some examples, values forthe signal parameters are determined as continuous time functions. Insome examples, values for the signal parameters are determined assampled points.

Transmitter 110 may also receive values for signal parameters; receivevalues for signal corrections from a previous calculation, if available;sample antenna current from a transducer, as an analog signal; digitizethe analog signal with an analog-to-digital converter, synchronized to aprecise time reference signal; determine values of signal parameters ofan antenna current; compare signal parameters of the antenna current tothe signal parameters; determine values of the signal corrections;output values of the signal corrections; and store values of the signalcorrections in a memory device.

Transmitter 110 may be an example of, or include aspects of, thecorresponding element or elements described with reference to FIG. 2.

Receiver 115 may include a matched filter configured to process thecontinuous, constant-power chirped-FM spread spectrum signal. In someexamples, the matched filter yields correlation of the base modulationand the data modulation to defined reference modulations.

In some examples, the receiver 115 further includes: means fordetermining a relative time of arrival of the continuous, constant-powerchirped-FM spread spectrum signal from the transmitter 110 within onemicrosecond; means for determining which data symbol values are likelyencoded in the continuous, constant-power chirped-FM spread spectrumsignal; and means for determining whether data symbols encoded in thecontinuous, constant-power chirped-FM spread spectrum signal arecorrupted. In some examples, the receiver 115 includes at least oneadditional matched filer for each base modulation frequency.

In some examples, forward error correction is used by the receiver 115to compensate for symbol errors resulting from received noise, jammingor interfering signals, or signals from other transmitters 110 in thesystem. In some examples, a set of parity symbols are appended to eachblock of data symbols. In some examples, where likely corrupted symbols(data or parity) are marked as erased. In some examples, where erasedsymbols are corrected, requiring a single parity symbol each to correct.In some examples, error symbols, not detected a priori as corrupted, aredetected and corrected, requiring two parity symbols each to detect andcorrect. In some examples, where a forward error correction code may bea Reed-Solomon code.

In some examples, the receiver 115 includes a multi-element antennaconfigured to allow a received signal to be processed and combined tosteer a null or maximum in a direction of an undesired or desiredtransmitter 110, and further configured to allow the received signal tobe processed in such a way as to determine an approximate direction of agiven transmitter 110.

Receiver 115 may be an example of, or include aspects of, thecorresponding element or elements described with reference to FIG. 3.

FIG. 2 shows an example of a transmitter 200 in accordance with aspectsof the present disclosure. Transmitter 200 may be an example of, orinclude aspects of, the corresponding element or elements described withreference to FIG. 1. Transmitter 200 may include base coded modulator205, data coded modulator 210, controller 215, variable power supply220, stepped power stage 225, band pass filter 230, antenna 235, monitor240, system control 245, and correction calculator 250.

Base coded modulator 205 may be configured to generate a basemodulation. In some examples, the base modulation includes a periodicfrequency modulation (FM) waveform. In some examples, the basemodulation is the periodic frequency modulation (FM) waveform selectedfrom the group of waveforms consisting of a triangle waveform, a ramp(sawtooth) waveform, a sinusoid waveform, and combinations of one ormore of such waveforms. In some examples, a base modulation frequencyfor each transmitter 200 in the array of transmitters is selected from aset of values.

Data coded modulator 210 may be configured to generate a datamodulation. In some examples, the data modulation includes a continuousfrequency-shift keying signal. In some examples, the continuousfrequency-shift keying signal encodes at least one data symbol perperiod of the periodic frequency modulation (FM) waveform.

In some examples, the continuous frequency-shift keying signal is shapedwith a window function. In some examples, the window function isselected from the group of functions consisting of Hann, Hamming,Blackman and Nutall. In some examples, the data modulation includesoperational data including timing offsets, nominal transmitter antennacenter position, and other information required for determination ofposition, navigation and time.

In some examples, the data modulation includes authentication data forallowing a receiver to validate that a message was sent by an authorizedtransmitter and was not corrupted or modified. In some examples, thedata modulation includes differential corrections that encodetime-varying signal propagation differences and other system errors fromnominal, allowing a receiver to correct these errors resulting ingreater accuracy. In some examples, the data modulation includesaltimeter corrections used by a receiver along with a local barometricpressure measurement to provide 3-dimensional position information.

FIG. 3 shows an example of a receiver 300 in accordance with aspects ofthe present disclosure. Receiver 300 may be an example of, or includeaspects of, the corresponding element or elements described withreference to FIG. 1. Receiver 300 may include digital signal processor305 and analog digital converter 320. Receiver 300 may also includeamplifier(s) 325 and antenna(s) 330.

In some examples, the digital signal processor 305 receives and decodesreceived signals, which, after decoding, are re-created by digitalsynthesis and subtracted from other received signals, and processed todetermine other transmitted signals, where co-channel interference isreduced. In some examples, the digital signal processor 305 isconfigured to use forward error correction to compensate for symbolerrors.

In some examples, the digital signal processor 305 receives and decodesreceived signals, to provide position, navigation, or timinginformation. In some examples, the digital signal processor 305 receivesand decodes received signals, to provide information selected from thegroup consisting of: position, course, course error, heading, velocity,acceleration, speed, time, distance to a next waypoint, a projectedchange in course or heading, time and frequency, message authentication.

Digital signal processor 305 may include matched filter 310 and decoder315. In some examples, at least one matched filter 310 coupled to thedigital signal processor 305, the at least one matched filter 310configured to decode the base modulation and data-encoded modulation andprovide a correlation function for received signals received from atleast three geographically-spaced transmitters.

FIG. 4 shows an example of modulation signals of a transmitter inaccordance with aspects of the present disclosure. The example shownincludes base modulation 400, data modulation 405, and total modulation410.

FIG. 5 shows an example of carrier signals of a transmitter inaccordance with aspects of the present disclosure. The example shownincludes stepped sinusoid wave 500 and filtered output wave 505.

FIG. 6 shows an example of active/reactive power ratios for an antennaand a transmitter in accordance with aspects of the present disclosure.Graph 600 may include antenna ratio 605 (solid line) and transmitterratio 610 (dashed line).

FIG. 7 shows an example of a process for low-frequency radio navigationutilizing continuous signal transmission in accordance with aspects ofthe present disclosure. In some examples, these operations may beperformed by a system including a processor executing a set of codes tocontrol functional elements of an apparatus. Additionally oralternatively, the processes may be performed using special-purposehardware. Generally, these operations may be performed according to themethods and processes described in accordance with aspects of thepresent disclosure. For example, the operations may be composed ofvarious substeps, or may be performed in conjunction with otheroperations described herein.

At step 700, the system may receive values for modulating signalparameters. In some cases, the operations of this step may be performedby a transmitter as described with reference to FIGS. 1 and 2.

At step 705, the system may receive values for modulation signalcorrections. In some cases, the operations of this step may be performedby a transmitter as described with reference to FIGS. 1 and 2.

At step 710, the system may receive a precise time reference signal. Insome cases, the operations of this step may be performed by atransmitter as described with reference to FIGS. 1 and 2.

At step 715, the system may determine resulting modulation parameters,including frequency and phase angle. In some cases, the operations ofthis step may be performed by a transmitter as described with referenceto FIGS. 1 and 2.

At step 720, the system may determine times when the direct digitalstepped synthesizer should step to next levels. In some cases, theoperations of this step may be performed by a transmitter as describedwith reference to FIGS. 1 and 2.

At step 725, the system may output one or a set of digital signals forcontrolling an output of the direct digital stepped synthesizer, as afunction of time. In some cases, the operations of this step may beperformed by a transmitter as described with reference to FIGS. 1 and 2.

FIG. 8 shows an example of a process for low-frequency radio navigationutilizing continuous signal transmission in accordance with aspects ofthe present disclosure. In some examples, these operations may beperformed by a system including a processor executing a set of codes tocontrol functional elements of an apparatus. Additionally oralternatively, the processes may be performed using special-purposehardware. Generally, these operations may be performed according to themethods and processes described in accordance with aspects of thepresent disclosure. For example, the operations may be composed ofvarious substeps, or may be performed in conjunction with otheroperations described herein.

At step 800, the system may receive values for signal parameters. Insome cases, the operations of this step may be performed by atransmitter as described with reference to FIGS. 1 and 2.

At step 805, the system may receive values for signal corrections from aprevious calculation, if available. In some cases, the operations ofthis step may be performed by a transmitter as described with referenceto FIGS. 1 and 2.

At step 810, the system may sample antenna current from a transducer, asan analog signal. In some cases, the operations of this step may beperformed by a transmitter as described with reference to FIGS. 1 and 2.

At step 815, the system may digitize the analog signal with ananalog-to-digital converter, synchronized to a precise time referencesignal. In some cases, the operations of this step may be performed by atransmitter as described with reference to FIGS. 1 and 2.

At step 820, the system may determine values of signal parameters of anantenna current. In some cases, the operations of this step may beperformed by a transmitter as described with reference to FIGS. 1 and 2.

At step 825, the system may compare signal parameters of the antennacurrent to the signal parameters. In some cases, the operations of thisstep may be performed by a transmitter as described with reference toFIGS. 1 and 2.

At step 830, the system may determine values of the signal corrections.In some cases, the operations of this step may be performed by atransmitter as described with reference to FIGS. 1 and 2.

At step 835, the system may output values of the signal corrections. Insome cases, the operations of this step may be performed by atransmitter as described with reference to FIGS. 1 and 2.

At step 840, the system may store values of the signal corrections in amemory device. In some cases, the operations of this step may beperformed by a transmitter as described with reference to FIGS. 1 and 2.

Some of the functional units described in this specification have beenlabeled as modules, or components, to more particularly emphasize theirimplementation independence. For example, a module may be implemented asa hardware circuit comprising custom very large scale integration (VLSI)circuits or gate arrays, off-the-shelf semiconductors such as logicchips, transistors, or other discrete components. A module may also beimplemented in programmable hardware devices such as field programmablegate arrays, programmable array logic, programmable logic devices or thelike.

Modules may also be implemented in software for execution by varioustypes of processors. An identified module of executable code may, forinstance, comprise one or more physical or logical blocks of computerinstructions that may, for instance, be organized as an object,procedure, or function. Nevertheless, the executables of an identifiedmodule need not be physically located together, but may comprisedisparate instructions stored in different locations which, when joinedlogically together, comprise the module and achieve the stated purposefor the module.

Indeed, a module of executable code could be a single instruction, ormany instructions, and may even be distributed over several differentcode segments, among different programs, and across several memorydevices. Similarly, operational data may be identified and illustratedherein within modules, and may be embodied in any suitable form andorganized within any suitable type of data structure. The operationaldata may be collected as a single data set, or may be distributed overdifferent locations including over different storage devices, and mayexist, at least partially, merely as electronic signals on a system ornetwork.

While the invention herein disclosed has been described by means ofspecific embodiments, examples and applications thereof, numerousmodifications and variations could be made thereto by those skilled inthe art without departing from the scope of the invention set forth inthe claims.

What is claimed is:
 1. A low-frequency radio navigation systemcomprising: a transmitter comprising: a base coded modulator configuredto generate a base modulation; a data coded modulator configured togenerate a data modulation; and wherein the transmitter radiates acontinuous, constant-power chirped-FM spread spectrum signal,comprising: the base modulation; and the data modulation, wherein thedata modulation is orthogonal to the base modulation.
 2. Thelow-frequency radio navigation system of claim 1, wherein: said basemodulation comprises a periodic frequency modulation (FM) waveform. 3.The low-frequency radio navigation system of claim 2, wherein: said basemodulation is the periodic frequency modulation (FM) waveform selectedfrom the group of waveforms consisting of a triangle waveform, a ramp(sawtooth) waveform, a sinusoid waveform, and combinations of one ormore of such waveforms.
 4. The low-frequency radio navigation system ofclaim 2, wherein: said data modulation comprises a continuousfrequency-shift keying signal.
 5. The low-frequency radio navigationsystem of claim 4, wherein: said continuous frequency-shift keyingsignal encodes at least one data symbol per period of said periodicfrequency modulation (FM) waveform.
 6. The low-frequency radionavigation system of claim 5, wherein: said continuous frequency-shiftkeying signal is shaped with a window function.
 7. The low-frequencyradio navigation system of claim 2, further comprising: a receivercomprising a matched filter configured to process the continuous,constant-power chirped-FM spread spectrum signal.
 8. The low-frequencyradio navigation system of claim 7, wherein: said matched filter yieldscorrelation of the base modulation and the data modulation to definedreference modulations; and said receiver further comprises: means fordetermining a relative time of arrival of said continuous,constant-power chirped-FM spread spectrum signal from the transmitterwithin one microsecond; means for determining which data symbol valuesare likely encoded in said continuous, constant-power chirped-FM spreadspectrum signal; and means for determining whether data symbols encodedin said continuous, constant-power chirped-FM spread spectrum signal arecorrupted.
 9. The low-frequency radio navigation system of claim 7,wherein: said transmitter shares a frequency band and carrier frequencywith a plurality of other transmitters in an array of transmitters; abase modulation frequency for each transmitter in the array oftransmitters is selected from a plurality of values; the receivercomprises at least one additional matched filer for each base modulationfrequency; and signals from said transmitter and said plurality of othertransmitters are identified and separated in said receiver.
 10. Thelow-frequency radio navigation system of claim 7, wherein: forward errorcorrection is used by said receiver to compensate for symbol errorsresulting from received noise, jamming or interfering signals, orsignals from other transmitters in the system; a plurality of paritysymbols are appended to each block of data symbols; wherein likelycorrupted symbols (data or parity) are marked as erased; wherein erasedsymbols are corrected, requiring a single parity symbol each to correct;wherein error symbols, not detected a priori as corrupted, are detectedand corrected, requiring two parity symbols each to detect and correct;and wherein a forward error correction code may be a Reed-Solomon code.11. The low-frequency radio navigation system of claim 2, wherein: saiddata modulation includes operational data comprising timing offsets,nominal transmitter antenna center position, and other informationrequired for determination of position, navigation and time.
 12. Thelow-frequency radio navigation system of claim 2, wherein: said datamodulation includes authentication data for allowing a receiver tovalidate that a message was sent by an authorized transmitter and wasnot corrupted or modified.
 13. The low-frequency radio navigation systemof claim 2, wherein: said data modulation includes differentialcorrections that encode time-varying signal propagation differences andother system errors from nominal, allowing a receiver to correct theseerrors resulting in greater accuracy.
 14. The low-frequency radionavigation system of claim 2, wherein: said data modulation includesaltimeter corrections used by a receiver along with a local barometricpressure measurement to provide 3-dimensional position information. 15.The low-frequency radio navigation system of claim 1, wherein: transmitenergy is spread over a fraction of a frequency band while minimizingpower outside of the frequency band, wherein said fraction of thefrequency band is 50% or greater and said power outside of saidfrequency band is less than 1%.
 16. A low-frequency radio navigationsystem comprising: a receiver comprising: a digital signal processor;and wherein at least one matched filter is coupled to the digital signalprocessor, the at least one matched filter configured to decode a basemodulation and a data-encoded modulation and provide a correlationfunction for received signals received from at least threegeographically-spaced transmitters.
 17. The low-frequency radionavigation system of claim 16, wherein: the digital signal processorreceives and decodes received signals, to provide position, navigation,or timing information.
 18. The low-frequency radio navigation system ofclaim 17, wherein: said digital signal processor receives and decodesreceived signals, to provide information selected from the groupconsisting of: position, course, course error, heading, velocity,acceleration, speed, time, distance to a next waypoint, a projectedchange in course or heading, time and frequency, message authentication.19. A low-frequency radio navigation system comprising: a firsttransmitter at a first location, the first transmitter comprising: afirst base coded modulator configured to generate a first basemodulation; and a first data coded modulator configured to generate afirst data modulation; wherein the first transmitter radiates a firstcontinuous, constant-power chirped-FM spread spectrum signal,comprising: the first base modulation; and the first data modulation,wherein the first data modulation is orthogonal to the first basemodulation; a second transmitter at a second location, the secondtransmitter comprising: a second base coded modulator configured togenerate a second base modulation; and a second data coded modulatorconfigured to generate a second data modulation; wherein the secondtransmitter radiates a second continuous, constant-power chirped-FMspread spectrum signal, comprising: the second base modulation; and thesecond data modulation, wherein the second data modulation is orthogonalto the second base modulation; and a third transmitter at a thirdlocation, the third transmitter comprising: a third base coded modulatorconfigured to generate a third base modulation; and a third data codedmodulator configured to generate a third data modulation; wherein thethird transmitter radiates a third continuous, constant-power chirped-FMspread spectrum signal, comprising: the third base modulation; and thethird data modulation, wherein the third data modulation is orthogonalto the third base modulation.